# Thread: Trying to help my brother.

1. ## Trying to help my brother.

I am a seasoned mech eng and for whatever reason this problem is kicking my butt. Here goes.

Find the smallest integer X so that 252*X is a perfect cube.

Ok so you say y^3=252*X and thats as far as I got. Cant take derivatives since this is just trig, so Im stumped. Please help.

3. Originally Posted by lewisb13
I am a seasoned mech eng and for whatever reason this problem is kicking my butt. Here goes.

Find the smallest integer X so that 252*X is a perfect cube.

Ok so you say y^3=252*X and thats as far as I got. Cant take derivatives since this is just trig, so Im stumped. Please help.
$\displaystyle 252=2^2 3^2 7$

For $\displaystyle x \times 252$ to be a perfect cube every prime factor in its prime decomposition must appear with power $\displaystyle 3$. So $\displaystyle x=2 \times 3 \times 7^2$ is the smallest positive integer $\displaystyle x$ that makes $\displaystyle x \times 252$ a perfect cube.

CB

4. Man thank you so much. That seems like some pretty advanced stuff to me. Geez.

5. 10char